马世晓在书法界的排名:两道高数题

来源：百度文库编辑：高校问答时间：2024/05/03 22:53:22

The lengths of the sides of a square are increasing at a constant rate of 2 feet/min.In term of the perimeter,p,what is the rate of change of the area of the square in square feet per minute?

A.p B.-p C.2p D.4p E.8p

From the values of f shown ,estimate f'(2)

x 1.92 1.94 1.96 1.98 2.00
f(x) 6.00 5.00 5.40 5.10 5.00

另外想请问
Evaluating limits
Rate of change
Differentials and linear apprpximation
Basic properties of integrals
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#1
let length of each side be s
perimeter be p
and area be A
A=s^2
dA/dt = 2s (ds/dt)
since s=p/4 and ds/dt=2
dA/dt=2(p/4)(2)=p
the answer's A

#2
use the slope of the secant line from x=1.98 to x=2.00 (this is not exact, but that's the best approximation u can get from the table)
f'(2)≈(5.00-5.10)/(2.00-1.98)

also, for #2, the question has to state that the function's differentiable

7月6日 19:49 题1答案：1的正弦加1的余弦减2的余弦再减2倍2的正弦，然后加3/2.
题2:对方程两边积分得x^3+y^3+c=0,由已知得y=(2-x^3)^(1/3).
题3:求二重积分得F=15pg,(p表示水的密度，g表示重力加速度）．

两道高数题